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While mostly skill, Scrabble does of course have that chance element. You could lose to an inferior play or beat a more skilled player based upon tile distribution in the game. Is there any system out there which adjusts the score at the end based upon the tiles that each player has drawn?

This could be for example one player got all 4 S tiles and both blank tiles and would be expected to score highter. Or it could be one player played 55 tiles and the other played 45 tiles during the course of a match. Maybe even handicap systems based upon the players respective ratings entering the match where the weaker player gets and additional 10 or 20 points.

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Duplicate scrabble Is a form of scrabble that is highly normalised and the standard form for competitive play in French. It can involve an arbitrary number of players who are not "competing" on the board, but only to find the highest score.

To eliminate some of the randomness and even out the game, you could try a few different things. Some of ideas I'm listing are for cases of different skill levels, and some are for making the game even between relatively equal skill players.

Just as a caveat, I've come up with all of these ideas after playing a lot of scrabble, and I don't usually play with any of them because I feel like they break the game.

1.If one player is better at winning with certain word lengths (ie his 2 and 3 word knowledge is better than his opponents)

2.If one player somehow gets all of the 10 point and 8 point letters and is able to use them for extremely high scoring:

Scale the scoring:
You'd need to keep track of each turn, and each word played/scored on during that turn.
At the end of the game, you normalize based on the rarity of the tiles you played. The player who didn't play any 10's will have two of his highest scoring tiles bumped up to 10 points points, if there is more than a 3 way tie between his top scoring tiles, then the opponent chooses which ones get bumped up. The same goes for if a player didn't play any 8's, or 5's. No scaling needs to be done for letters with less score.

3.Disallow Hooking scores for experienced players (only letters in one direction can be scored on a single turn)

4.Remove Z, Q, J, X, K, Blanks, S and any other letters you find useful. Shake up the remaining tiles and distribute them evenly between the two players. Then divide the remaining high scoring or highly useful tiles between the two players. This will help eliminate randomness. You can always play a mirror match after, with the tiles your opponent played with.

5.Both players play with Identical sets of Scrabble tiles. The tiles are still drawn randomly from a pouch (or other container).

6.Play best of 3 or more. This is usually a good remedy that eliminates randomness as an excuse for losing/winning. Take the three scores and normalize them so they are evenly weighted

7.Tile Swaps when you have no vowels will not end your turn, Tile swaps when you swap 3 of a kind will not end your turn. This also means you should limit Tile swaps to once per turn.

8.Prove a word can't be played with x tiles from your stand. You place the tiles in front of the other player. If he can't form (or doesn't want to form) a word with them within a certain time limit then you swap the letters and continue your turn, you can do this once per turn. If the opponent can create a word out of your letters, then you must play that word on the board, but do not get any points for it. This kind of system is usually in favor of the more skilled wordsmith.

9.Standby Tiles: Leave a second set of scrabble tiles on standby. Whenever a player plays a word the opponent can choose one letter in that word, and pull it from the standby set of tiles to be used in their next turn.

A variant of this would be to swap one of your tiles with a tile from that set. In this way, there always exists a set of tiles to swap from.

This means you'll never be denied access to any one specific tile in a game.

When playing with my kids I spot them points. As early teenagers around 120 points was right, my 18 year old son is down to about a 65 spot now.

I embarrassed myself by offering a 60 point spot to my cousin's daughter two years ago, and she beat me by more than the spot. However that is the last time I will also allow her access to a printed word list. ;-)